Sr Examen
Expresión PV(~p→(qV(q→~r)))
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Solución
Ha introducido
[src]
p∨((¬p)⇒(q∨(q⇒(¬r))))
$$p \vee \left(\neg p \Rightarrow \left(q \vee \left(q \Rightarrow \neg r\right)\right)\right)$$
Solución detallada
$$q \Rightarrow \neg r = \neg q \vee \neg r$$
$$q \vee \left(q \Rightarrow \neg r\right) = 1$$
$$\neg p \Rightarrow \left(q \vee \left(q \Rightarrow \neg r\right)\right) = 1$$
$$p \vee \left(\neg p \Rightarrow \left(q \vee \left(q \Rightarrow \neg r\right)\right)\right) = 1$$
$$q \vee \left(q \Rightarrow \neg r\right) = 1$$
$$\neg p \Rightarrow \left(q \vee \left(q \Rightarrow \neg r\right)\right) = 1$$
$$p \vee \left(\neg p \Rightarrow \left(q \vee \left(q \Rightarrow \neg r\right)\right)\right) = 1$$
Tabla de verdad
+---+---+---+--------+ | p | q | r | result | +===+===+===+========+ | 0 | 0 | 0 | 1 | +---+---+---+--------+ | 0 | 0 | 1 | 1 | +---+---+---+--------+ | 0 | 1 | 0 | 1 | +---+---+---+--------+ | 0 | 1 | 1 | 1 | +---+---+---+--------+ | 1 | 0 | 0 | 1 | +---+---+---+--------+ | 1 | 0 | 1 | 1 | +---+---+---+--------+ | 1 | 1 | 0 | 1 | +---+---+---+--------+ | 1 | 1 | 1 | 1 | +---+---+---+--------+